While I'm not the plugin author, the message would seem to indicate that the plugin pre-install check routine may simply be alerting you to the fact that the open base directory restriction in PHP, has been enabled in your hosting environment.
In a nutshell, it limits file access by php scripts to a designated directory. It's completely possible that in your case, "Open Base Dir: On - Fail" is nothing more that a warning message from the plugin that Open Base Dir is "turned on" in php on your host - especially if you haven't actually encountered the "open_basedir restriction in effect" message while using the plugin. It may not be an issue at all.
That's just my best-guess, mind you, but I'm sure the plugin author can give you a better answer. You might be able to get a quicker response from them by contacting support on their site.
Good luck to you!